It looks like you're trying to solve the equation \( \frac{x}{2} + \frac{x^2}{8} = 0 \). Let's go step-by-step to solve for \( x \).

1. Start with the given equation:
\[
\frac{x}{2} + \frac{x^2}{8} = 0
\]

2. To eliminate the fractions, multiply every term by 8 (the least common denominator):
\[
8 \cdot \frac{x}{2} + 8 \cdot \frac{x^2}{8} = 8 \cdot 0
\]

3. This simplifies to:
\[
4x + x^2 = 0
\]

4. Rearrange the equation:
\[
x^2 + 4x = 0
\]

5. Factor out an \( x \) from the left side:
\[
x(x + 4) = 0
\]

6. Set each factor equal to zero:
\[
x = 0 \quad \text{or} \quad x + 4 = 0
\]

7. Solve each equation:
- \( x = 0 \)
- \( x + 4 = 0 \) which gives \( x = -4 \)

Therefore, the solutions to the equation are \( x = 0 \) and \( x = -4 \).